We study the joint distribution of the set of all marginals of a random Wishart matrix acting on a tensor product Hilbert space. We compute the limiting free mixed cumulants of the marginals, and we show that in the balanced asymptotical regime, the marginals are asymptotically free. We connect the matrix integrals relevant to the study of operators on tensor product spaces with the corresponding classes of combinatorial maps, for which we develop the combinatorial machinery necessary for the asymptotic study. Finally, we present some applications to the theory of random quantum states in quantum information theory.

中文翻译：

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多方随机量子态边缘的联合分布

我们研究了作用于张量积希尔伯特空间的随机 Wishart 矩阵的所有边际集合的联合分布。我们计算了边际的限制自由混合累积量，并且我们证明了在平衡渐近方案中，边际是渐近自由的。我们将与张量积空间上的算子研究相关的矩阵积分与相应类别的组合映射联系起来，为此我们开发了渐近研究所需的组合机制。最后，我们介绍了量子信息论中随机量子态理论的一些应用。